Drivers of Antarctic sea ice advance

Antarctic sea ice is mostly seasonal. While changes in sea ice seasonality have been observed in recent decades, the lack of process understanding remains a key challenge to interpret these changes. To address this knowledge gap, we investigate the processes driving the ice season onset, known as sea ice advance, using remote sensing and in situ observations. Here, we find that seawater freezing predominantly drives advance in the inner seasonal ice zone. By contrast, in an outer band a few degrees wide, advance is due to the import of drifting ice into warmer waters. We show that advance dates are strongly related to the heat stored in the summer ocean mixed layer. This heat is controlled by the timing of sea ice retreat, explaining the tight link between retreat and advance dates. Such a thermodynamic linkage strongly constrains the climatology and interannual variations, albeit with less influence on the latter.


Analysis of the Supplementary Figures
The sea ice concentration budget at the date of advance (da) has large uncertainties, hence we integrate it in time over a time window spanning part of the sea ice season.In Supplementary Fig. 1, we find that the sea ice concentration budget-derived limit between the inner and outer zones does not strongly depend on the size of the time integration window, suggesting it is robust enough for the present analysis.
In Supplementary Fig. 2, we evaluate the robustness of the sea surface temperature at date of advance (SSTda) across time periods and SST products.We find that SSTda slightly differs according to the averaging period (2003-2010 or 1982-2018) or the product (ESA CCI or Reynolds').However, the effect of the inner-outer zone limit is always visible.Hence, the SST-based inner-outer zone limit is also robust, we reckon.Furthermore, SSTda -Tf (where Tf is the freezing temperature) is generally higher than uncertainty, and even more so in the outer zone.This is consistent with a higher SSTda in the outer zone compared to the inner zone.In the inner zone, higher than uncertainty (SSTda -Tf) could be due to a spatial averaging effect: a 15% ice covered grid point of 25 km 2 is not necessarily at the freezing point over its full surface.
In Supplementary Fig. 3, we test whether available in-situ hydrographic records support satellite-based findings regarding the SST at the date of advance.In-situ SST measurements are from float  and marine mammal-borne sensors (2004-2020, see Methods).In situ SSTs were collocated with the passive-microwave dates of sea ice advance for the corresponding sampling year.Only 28 records correspond to an available date of advance within 3 days in the corresponding satellite pixel.
We find the histograms of Supplementary Fig. 2 from these 28 in situ records and their satellite counterparts (ESA CCI) SSTda to be compatible.
In Supplementary Fig. 4, we examine the temperature contribution to the stratification at the base of the mixed layer during the sea ice advance season ( " # ). " # is proportional to the vertical temperature gradient at the base of the mixed layer and defined as: , where  , is the temperature at the base of the mixed layer, , the thermal expansion coefficient at constant pressure: and , the gravity acceleration. " # < 0 ( " # > 0) indicates a negative (positive) temperature gradient and an unstable (stable) temperature profile at the base of the mixed layer.
We find that, in the outer zone, the temperature profile at the base of the mixed layer is unstable during the three first months of the advance season ( " # < 0), indicating a possible entrainment of warm waters into the mixed layer during these months.This entrainment might contribute to the excess of heat causing the high SSTda and the resulting melting in the outer zone.
In Supplementary Fig. 5, we show a strong correspondence between the seasonal maximum of mixed layer heat content (MLHmax) and the net radiative flux absorbed by the ocean.The latter is itself constrained by the date of sea ice retreat, which suggests a large control of MLHmax by radiative heating of the upper ocean and explains why MLHmax is tightly linked to the date of sea ice retreat (dr) (see Figure 3c).
In Supplementary Fig. 6, we test the strength of the dr-MLHmax-da linear relationships in the outer zone.We find that these relationships are significantly weaker in the outer zone than in the inner zone (see Fig. 3), according to Fisher's Z-test at a 0.01 significance level.However, the MLHmax-da relation still explains a large part (83%) of the variance in the climatological date of advance.By contrast, the dr-da relation is weaker than the dr-MLHmax and the MLHmax-da relations, in the outer zone.
In Supplementary Fig. 7, we show that the weaker dr-da relation in the outer zone might be due to different spatial distributions of the errors in the dr-MLHmax and the MLHmax-da linear regressions.

Figure 1 |
Sensitivity of the sea ice concentration-budget-based regions to the time-integration window.a shows the spatial distribution of three regions defined based on the budget: melting (Th < 0; orange), dominant dynamics (|Dy/Th| > 1; yellow and orange), dominant thermodynamics (|Dy/Th| < 1; blue).The budget is averaged after the date of sea ice advance (da), over a time window of unconstrained duration, which influence is tested here (values of 15, 30, 40 and 60 days).Grid points where the budget is not defined because of missing ice drift data are in grey and the perennial ice zone in white.b shows the fractional area of the aforementioned regions (in % of the seasonal ice zone), for the different integration time windows.Supplementary Figure 2 | Robustness of the inner-outer zone limit across time periods and sea surface temperature (SST) products.SST at the date of advance (SSTda) referenced to freezing temperature (Tf, assumed constant at -1.8°C), based on a ESA CCI SST, averaged over 2003-2010; b ESA CCI SST, averaged over 1982-2018; and c Reynolds' SST, averaged over 2003-2010.d Difference between SSTda and Tf and the uncertainty (e) on the ESA CCI SST analysis, averaged over 2003-2010.Corresponding frequency histograms are shown under each map in grey (a) or beige (b, c, d).In b and c, the grey histogram is the same as in a and used as a reference distribution.The black contour defines the limit between the inner and outer zones.White patches indicate regions out of the seasonal ice zone.